Prices would probably stay the same. The idea is undercutting items so they sell quicker would be because people pay less for the item, instead of the current system which penalises people for not undercutting.

Of course, I'd prefer it if they were just offline, anonymous bazaars even more.

A few years back, Squeenix released one of their census thingies which showed that the starter city auction houses were used primarily for crafting materials, and the Jueno AH for equipment and other battle related stuff. Ever since ToAU, crafters have had access to every guild in either Whitegate or Al Zahbi. There is literally no point in leaving Whitegate for any AH-related purpose. Furthermore, the remaining AHes have all deteriorated; they're now notorious for having wacky price fluctuations.

AH fees are still pointless gilsinks, either way.